AI 中文总结
研究具有截断结果的回归共形预测，指出现有方法不足，通过引入新不一致分数和校准方法应对挑战，刻画了方法的有限样本覆盖率等行为并与其他方法比较。
AI 中文摘要
我们研究了使用校准数据进行回归的共形预测，其中结果在已知固定阈值处进行双重截断（剪辑）。我们表明，现有方法在此设置下并不令人满意，因为它们产生的区间可能具有比期望更高的边际覆盖率，但对于通常能完全观察到结果的更容易预测的情况，却失去了条件覆盖率。这表明，共形预测通常的目标——边际覆盖率，在截断情况下可能不是理想目标。我们通过在这种权衡的两端引入新的不一致分数和校准方法来应对这一挑战：一种用于紧密的边际覆盖率，另一种是优先考虑条件覆盖率的两步法。我们在基础模型的适当一致性下刻画了它们的有限样本覆盖率和类似神谕的渐近行为，并将它们与现有方法的更直接改编进行了比较。
英文摘要
We study conformal prediction for regression using calibration data with outcomes that are doubly censored (clipped) at known fixed thresholds. We show that existing methods are unsatisfactory in this setting, as they yield intervals that may have higher marginal coverage than desired and yet lose conditional coverage precisely for the easier-to-predict cases whose outcomes are typically fully observed. This reveals that marginal coverage, the usual target of conformal prediction, may not be the ideal goal under clipping. We address this challenge by introducing a new nonconformity score and calibration methods at both ends of this trade-off: one for tight marginal coverage, and a two-step method that prioritizes conditional coverage. We characterize their finite-sample coverage and oracle-like asymptotic behavior under suitable consistency of the underlying model, and we compare them to more direct adaptations of existing approaches.
